Such a pressure welding device is known from practice. It may be configured as a friction welding device or as a welding device with an arc moved rotatingly magnetically and has, in both variants, a plasticization device and an upsetting device each as well as component mounts for the components to be welded together. It further has a machine frame, on which a machine head with a component mount is arranged movably. An associated additional component mount is likewise arranged movably on the machine frame. Single-head machines and double-head machines are known from practice, and two machine heads and one or two additional or central component mounts are present in the latter case. A possibly necessary finishing of the welded part is carried out separately and at another location in the case of the prior-art pressure welding devices.